Initial animated particles on a force field path: How to control/hide?
Texture mask to hide unwanted particles in center (red outline) but keep surrounding visible (green outline).

Emitter object's coordinates controls spherical texture which gradient splits material in two shaders: default and invisible (holdout or transparent BSDF for your choice).

Holdout is easier for render but needs compositing, while transparent with many overlayed particles need many transparency bounces to get clean results.